The Treaty will determine in which State(s) a particular source of income or gains will, or may, be taxed.

Unilateral relief is not "available anyway".

Unilateral relief is available where the specific source of income etc is not provided for in the Treaty. If credit is available, even if not claimed, under the Treaty then no unilateral relief (at least not by credit).

Also, unilateral credit relief (and Treaty credit relief) is available only if the foreign tax has been deducted/paid in accordance with the laws etc of that State. If it hasn't, relief by deduction instead should be available.